A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?

Possibilities:

1.

The number rolled can be a 2.

2.

The number rolled can be a 5.

Events:

These events are mutually exclusive since they cannot occur at the same time.

Probabilities:

How do we find the probabilities of these mutually exclusive events? We need a rule to
guide us.

Addition Rule 1:

When two events, A and B, are mutually exclusive, the probability that A or B will occur
is the sum of the probability of each event.

P(A or B) = P(A) + P(B)

Let's use this addition rule to find the probability for Experiment 1.

Experiment 1:

A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?

Probabilities:

P(2)

=

1

6

P(5)

=

1

6

P(2 or 5)

=

P(2)

+

P(5)

=

1

+

1

6

6

=

2

6

=

1

3

Experiment 2:

A spinner has 4 equal sectors colored yellow, blue, green, and red. What is the
probability of landing on red or blue after spinning this spinner?

Probabilities:

P(red)

=

1

4

P(blue)

=

1

4

P(red or blue)

=

P(red)

+

P(blue)

=

1

+

1

4

4

=

2

4

=

1

2

Experiment 3:

A glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. If a
single marble is chosen at random from the jar, what is the probability that it is yellow or green?

Probabilities:

P(yellow)

=

4

10

P(green)

=

3

10

P(yellow or green)

=

P(yellow)

+

P(green)

=

4

+

3

10

10

=

7

10

In each of the three experiments above, the events are mutually exclusive. Let's look
at some experiments in which the events are non-mutually exclusive.

Experiment 4:

A single card is chosen at random from a standard deck of 52 playing
cards. What is the probability of choosing a king or a club?

Probabilities:

P(king or club)

=

P(king)

+

P(club)

-

P(king of clubs)

=

4

+

13

-

1

52

52

52

=

16

52

=

4

13

In Experiment 4, the events are non-mutually exclusive. The addition causes the king of
clubs to be counted twice, so its probability must be subtracted. When two events are non-mutually exclusive, a
different addition rule must be used.

Addition Rule 2:

When two events, A and B, are non-mutually exclusive, the
probability that A or B will occur is:

P(A or B) = P(A) + P(B) - P(A and B)

In the rule above, P(A and B) refers to the overlap of the two events. Let's
apply this rule to some other experiments.

Experiment 5:

In a math class of 30 students, 17 are boys and 13 are girls. On a unit test,
4 boys and 5 girls made an A grade. If a student is chosen at random from the class, what is the
probability of choosing a girl or an A student?

Probabilities:

P(girl or A)

=

P(girl)

+

P(A)

-

P(girl and A)

=

13

+

9

-

5

30

30

30

=

17

30

Experiment 6:

On New Year's Eve, the probability of a person having a car accident is 0.09. The probability of a person driving while intoxicated is 0.32 and probability of a person having a car accident while intoxicated is 0.15. What is the probability of a person driving while intoxicated or having a car accident?

Probabilities:

P(intoxicated or accident)

=

P(intoxicated)

+

P(accident)

-

P(intoxicated and accident)

=

0.32

+

0.09

-

0.15

=

0.26

Summary:

To find the probability of event A or B, we must first determine whether the events are
mutually exclusive or non-mutually exclusive. Then we can apply the appropriate Addition
Rule:

Addition Rule 1:

When two events, A and B, are mutually exclusive, the
probability that A or B will occur is the sum of the probability of each event.

P(A or B) = P(A) + P(B)

Addition Rule 2::

When two events, A and B, are non-mutually exclusive, there is some
overlap between these events. The probability that A or B
will occur is the sum of the probability of each event, minus the probability of the
overlap.

P(A or B) = P(A) + P(B) - P(A and B)

Exercises

Directions: Read each question below. Select your answer by clicking on its button. Feedback to your answer
is provided in the RESULTS BOX. If you make a mistake, choose a different button.

1.

A day of the week is chosen at random. What is the probability of choosing a Monday or Tuesday?

None of the above.

RESULTS BOX:

2.

In a pet store, there are 6 puppies, 9 kittens, 4 gerbils and 7 parakeets. If a pet is chosen at random,
what is the probability of choosing a puppy or a parakeet?

1

None of the above.

RESULTS BOX:

3.

The probability of a New York teenager owning a skateboard is 0.37, of owning a bicycle is 0.81 and of owning both is 0.36. If a New York teenager is chosen at random, what is the
probability that the teenager owns a skateboard or a bicycle?

1.18
0.7
0.82
None of the above.

RESULTS BOX:

4.

A number from 1 to 10 is chosen at random. What is the probability of choosing a
5 or an even number?

All of the above.

RESULTS BOX:

5.

A single 6-sided die is rolled. What is the probability of rolling a number greater than 3 or an even
number?